The fuel rods in a BWR core are grouped in bundles with spacers and usually also end plates to keep the fuel rods in each bundle in a predetermined geometry. The predetermined rod lattice may be regular or irregular and even change axially. The bundles are then enclosed by channels to direct the coolant flow upward and give the fuel arrangement mechanical and thermal hydraulic stability and facilitate handling and exchange of the fuel. The fuel rod bundle and the channel are often referred to as a fuel assembly as the handling unit. Each channel may also contain more than one fuel bundle and still be referred to as a fuel assembly. The channels may be square or hexagonal and have internal structures and features apart from end fittings. The fuel bundle may also vary considerably in size—from 24 to 144 fuel rods—and it may also contain special purpose rods such as tie rods, water rods, part length rods and burnable absorber rods. A multitude of fissile material enrichments both between and within the fuel rods is also common. The present invention is applicable to all of these fuel arrangements and their operation in the reactor.
As is well known to a person skilled in the art, in a BWR a cooling medium in the form of water flows through the fuel assemblies, which contain the fuel rods. The purpose of the water is to cool the fuel rods and to act as a neutron moderator. A mixture of steam and water is flowing through the fuel bundle, providing cooling for the rods by convective and boiling heat transfer. As the steam quality (the steam content fraction) of the coolant increases, the flow pattern is changing. At a certain point in the bundle, an annular flow pattern is formed. This implies existence of a thin liquid film on the surface of the rods, and a mixture of vapour and droplets in the channels between the rods. The existence of this film allows for efficient heat transfer from the rods to the coolant. This enables both effective steam generation and prevents the rods from overheating. The breakdown of this film is referred to as dryout.
In a BWR dryout should be avoided. Dryout deteriorates heat transfer from the fuel rods to the reactor cooling medium and therefore leads to an increased temperature of the walls of the fuel rods. The increased temperature can damage the fuel rods. If a BWR is operated at or above a certain high power, the so-called critical power (CP), dryout may thus occur. In order to avoid dryout, the reactor is therefore operated at, a lower power, such that a certain safety margin exists, the so-called dryout margin. A measure of the dryout margin is the critical power ratio (CPR). The CPR can be defined as the following ratio:CPR=(critical power)/(actual power)
The CPR can be calculated locally for a large number of points in the reactor core. The smallest value of the CPR in any point is called the minimum critical power ratio MCPR.
In the following critical power and critical heat flux and critical steam quality are treated as synonymous or equivalent entities as there exist straight forward physical transformation laws between them in steady state operation. With the coolant flow and the inlet enthalpy known the steam quality directly provides the fuel arrangement power with steam/water thermodynamic data and vice versa.
There are two common methods used to correlate critical power test data for BWR fuel assemblies. Both are based on observed functional dependencies between the experimental parameters. One is to correlate the critical power data with the critical heat flux and the other method is to correlate the critical power test data with critical steam quality and the so-called boiling length as the main variables
The critical heat flux correlation is based upon a so-called relaxed local conditions hypothesis. This type of correlation is based on Macbeth and Barnett's well known linear dependence between critical dryout power and subcooling at constant mass flux and pressure. The local condition hypotheses correlation has the following form:
ΦDO,z=f(P, D, G, XZ)
where
ΦDO,z=heat flux at dryout
P=system pressure
D=fuel hydraulic diameter
G=mass flux
Xz=steam quality at axial position z in reactor core
Linear dependencies between the parameters are established at least piecewise by use of fitting coefficients to the measured data. Combination of local dryout heat flux and heat balance allows calculation of critical power and includes implicitly the influence of axial heat flux distribution or power shape.
The other method is to correlate the critical steam quality (power) and capture the dependence of critical power on mass flux, pressure, inlet subcooling, and axial and radial power distributions. The terms in a critical quality-boiling length correlation are best-fit functions that describe the critical steam quality dependence on mass flux, outlet pressure, boiling length, annular length and R-factor based on the test data and has the following form:
XDO=f(G, P, BL, AL, R)
where
XDO=critical steam quality
G=mass flux
P=system pressure
BL=boiling length
AL=annular flow length
R=R-factor. It is typically postulated to capture the critical quality dependence on lateral flow and power distributions.
The critical power can be predicted from the steam quality by using the heat balance along the channel. This is an iterative process and includes the influence of axial shape implicitly. Critical power test data are correlated in the so-called critical quality-boiling length plane, i.e. critical power, mass flux, pressure and inlet sub-cooling data are converted to a relationship between steam quality at the location where dryout occurs and the so-called boiling length, BL. Boiling length is defined as the distance from the starting point of bulk boiling (Blen) to the end of heated length, EHL. Furthermore it has been shown that a critical quality—boiling length correlation with the annular boiling length, AL, as an additional correlation parameter implicitly handles the influence of the axial power shape on critical power properly. AL is the distance from the annular flow transition point to the end of heated length, EHL.
Dryout dependence on the local power distribution, cross section geometry, and the grid spacer configuration is handled through the use of a so-called R-factor. These R-factors are a measure of the dryout sensitivity of each rod. The limiting R-factor of a sub-bundle is the maximum of R-factors of its rods. In tests, the peak power rod has been systematically moved around in the sub-bundle in order to investigate the dryout sensitivity of rod positions. The large number of local power distributions tested has allowed a derivation of empirical additive constants to calculated R-factors.
The two common methods to correlate dryout data have with time and increasing demands for accuracy and validity range became complex. The correlations are basically linear forms (polynomials), but with many terms and regression coefficients trying to capture highly non-linear effects.
The document SE-C2-509 235 describes a method of estimating the risk for dryout in a BWR. In this method so-called transient phenomena are taken into account. A transient can for example occur when the coolant flow is reduced while maintaining the actual reactor power. This leads to a reduction of the CP. The method includes the use of a transient analyser. In the transient analyser the behavior of the nuclear reactor during a transient is simulated. The transient analyser calculates the reduction of the CP during transients.
EP-A1-1 221 701 describes a method and system for thermal-dynamic modeling and performance evaluation of a BWR core design. A data processing system is used to execute specific program routines that simulate the thermal operating characteristics of fuel rods within the reactor during a transient operational condition. The method employs a multi-dimensional approach for the simulation of postulated operational events or an anticipated operational occurrence which produces a transient condition in the reactor, such as might be caused by single operator error or equipment malfunction. Based on a generic transient bias and uncertainty in the change in critical power ratio, histograms of fuel rod critical power ratio are generated. Ultimately, the operating limit minimum critical power ratio of the reactor is evaluated from a histogram of probability calculations representing the number of fuel rods subject to a boiling transition during the transient condition. The histogram may be readily displayed by the data processing system and used to statistically demonstrate an operating limit minimum critical power ratio compliance of the reactor core design with official regulations.
Dryout properties in a real nuclear reactor application can be estimated on the basis of experiments in an experiment station. This experiment station is made to be similar to a part of a real reactor core, but no nuclear reaction takes place in the experiment station. The experiment station can include an experiment chamber in which a number of simulated nuclear fuel rods (but without the nuclear fuel material) are positioned relative to each other in the same manner (or a similar manner) to the fuel rods in a real nuclear reactor core. However, the number of fuel rods in the experiment station is usually much less than in a real reactor core that may contain from 40000 to 80000 or more rods. For example, 24 fuel rods can be used in the experiment station. These fuel rods can represent a sub-bundle of a bundle of fuel rods of a real fuel arrangement. The fuel rods in the experiment station are provided with electrical heater elements so that they can be heated to at least the same temperatures as the fuel rods in a real nuclear reactor. The electrical current to the heater elements can be varied in order to simulate different power levels and power distributions that can occur in a real nuclear reactor core. Furthermore, water is fed through the experiment chamber. The temperature, the mass flux of water, axial and radial power shapes and the pressure of the water can be varied in order to simulate different operation conditions and transient behavior.
The experiment station is provided with different measurement means in order to measure the mass flux, the pressure and the temperature at different positions in the experiment station. However, the number of measurement points and the different measurements that can be performed in a limited time is limited. It is therefore often difficult to estimate the dryout properties in a real nuclear reactor on the direct basis of such experiments.
Since the number of measurement points, and the number of different measurements that are carried out, are limited, it is necessary to find a model (often called a correlation) that predicts the behaviour of a nuclear fuel arrangement between and outside the conditions that have actually been measured in the experiment station. It is a difficult process to interpolate and extrapolate the result from the experiment to a real general description of the dryout behaviour with high accuracy in a real nuclear reactor.